John – "you are the pits of the world" – McEnroe's belief that he owes the Williams sisters, late of scabrous Compton, Los Angeles, a firm pre-Wimbledon lecture on the need for respect is uproariously funny and bizarre and sad. It is also right.

McEnroe, heaven knows, is not the first senior citizen of any walk of life required to tell a new generation to do what he says rather than what he did. Even now the old hell-raiser, for all the puckish humour and blazing savvy he applies as a commentator to the game he both thrilled and traumatised as tennis's version of an enervated Pol Pot complete with red headband, seems a little uncertain about the line which divides "kicking ass" and the rankest of bad manners. But it is harder to dispute McEnroe's nose for something more deeply disturbing in the story of the astonishing rise of Venus and Serena Williams.

McEnroe was denied membership of the All-England club at the height of his anarchy but his love of the game, or at least the engagement it brought to his searingly competitive nature, was never questioned. The same cannot be said of Venus and Serena Williams. However many times we hear of their eccentric father Richard's Svengali performance in lifting them from the shockingly narrow horizons of the crime-scarred neighbourhood of their youth, however much we marvel at the extraordinary athleticism of Venus and the probably superior ability of Serena, it is hard to clear our heads of the doubts.

They are doubts, primarily, about the sisters' place in the game; the doubts not of white, country-club America, or the stuffy grandees of the Centre Court, but of those who believe that great sports stars enter an unwritten contract to perform, as well as they can according to their lights, and in return they take their acclaim and their megabuck deals. It is not a negotiable thing, and certainly not something to be left to the discretion of an odd-ball character like Richard Williams.

Such questioning is dismissed by Williams Snr as racism. That was his reaction to the booing of Serena by an American crowd during a final in Indian Wells, one to which she had progressed after Venus had withdrawn rather than meet her sister in a semi-final, a decision provoked not – some claimed and the crowd believed – by nagging concern about an injury but by order of her father.

The Indian Wells controversy was a ripple which flowed all the way back to Wimbledon this time last year when Venus swept Serena, the reigning US Open champion, out of the semi-final in two perfunctory sets. Watching Serena produce such a strange, almost disconnected performance was rather like seeing a Derby favourite idling at Tattenham Corner.

The question that afterwards had to be asked the tearful Serena could scarcely have been less subtle: did your father ask you to throw the game? Her answer was chillingly equivocal. She said she could not answer for her family.

Venus's demeanour was also odd. Certainly she was in no mood to encourage the idea that, like Althea Gibson all those years before, she was ready to pick up the baton for the poor, black youth of America. "You do as much as you can," she said flatly, "You know we travel so much on the road. When you get home you only have 10 days. You can only have two days off. The rest of the days you have to practice. It's tough. We have two jobs, you know."

There was maybe a hint here of the attitude that progressed to the point at which McEnroe took such violent exception. McEnroe's complaint, it seems, is not so much that the Williams girls feel they are above the game but that they are separated from it in a way which is incomprehensible to the old tennis trench fighter. The idea that he might be manipulated and shaped in his every action by his father, a successful New York corporate lawyer, was certainly banished by a visit to McEnroe Snr's Manhattan office at a time when his son was rampaging so hard there seemed a danger that he might go into orbit. "John," said his father, "is a tremendous competitor who cares deeply about the game he plays, and that would have been so whatever sport he had taken up. As a boy he needed to win all the family games."

By comparison, Venus and Serena were dutifully compliant as their father led them to the public courts in Compton, where members of the Los Angeles Police Department are told they cannot go without back-up. The old, haunting picture is of the little girls clearing from the courts the abandoned syringes of drug-users. So if the sisters are accused of operating in tennis for what it can provide rather than for what they can give in return, part of you has to ask: How it could not be so? Where, as they see it, do their debts reside? In a game peopled almost exclusively by the white and the middle class, who not so long ago inhabited a different, unattainable world – or in the fractious, unpredictable nature of the man who propelled them into the rich pickings of a game they initially saw as alien if not outright hostile? In his maturity, McEnroe lists his leaders as the great men of the game, the Lavers and Rosewalls and Hoads. Venus's and Serena's leader, no-one can seriously doubt, is Richard Williams.

On the eve of last year's semi-final the girls' mother, Oracene, gave a rare interview during which she said that no words about the huge game they faced would come from either Venus or Serena. "They haven't spoken about this match and they won't say anything, either. Neither will I and neither will their father. Not a word will pass anyone's lips. I suppose you could say it is an unwritten rule in our house, but that's the way we do things. They'll just go out and play, congratulate each other and then talk about other things. When they're off the court they never, ever talk about tennis. It isn't going to change now. They may be competing against each other, but it's just another game. They're sisters and that comes first."

Did it come first when Serena, who already had a Grand Slam victory – a fact which gnawed at Venus so badly that some feared it was having a serious affect on her personality – so seriously underperformed? The American supermarket tabloid National Inquirer ran a story that it did, that the match was settled not by the play on the Centre Court but by an edict at the family breakfast table. The Inquirer may not be celebrated as a newspaper of record, but the story did not read so bizarrely to those who had been at Wimbledon on the day in question, who saw Serena's tears and heard her pointed refusal to deny the idea that the game had been influenced by more than current form.

It is something that will probably lie forever in the vaults of the family's new existence in one of the most luxurious corners of Florida. But it is hard to bury such a powerful whiff of intrigue, especially when the careers of Venus, who received a $40m (£29m) endorsement from a sports gear manufacturer last year after adding the US Open to her Wimbledon crown, and Serena are increasingly marked by a tendency to play the game only on their terms.

McEnroe thunders: "What they have achieved is great but they have no respect for anyone in the game. What people truly appreciate are those with a sense of history. Rod Laver helped give me my vision and I hope I passed some of that on to the next generation. I don't mind anyone walking on the court and kicking ass, but this is about more than that."

What it is really about, and what McEnroe passed on to the next generation, will always be matters of opinion. But if McEnroe so often behaved abominably, if he regularly psyched up himself at the expense of officials and, most vitally, his opponents, he gave all of his talent, and in the process no-one ever had to ask if he truly cared. As his father said that afternoon in his office, young John would not dream of yielding a game of checkers to a beloved grandmother.

Venus and Serena Williams are superb players, but as yet no one could begin to make such a claim on their behalf. That is always likely to remain at the heart of a troubling enigma.